# Эксперимент: Forward-Intersection Spectral Latent Dynamics (#635)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built forward_intersection.py with SVD nullspace intersections and normalized principal-angle filtering, plus mini_experiment.py for noisy least-squares snapshots. The toy predictions matched: the finite-tolerance transition occurred at alpha=0.26536 predicted versus between 0.263 and 0.270 observed, supported eigenvalue error was 2.22e-16, and exact intersection dimensions were 4 at alpha=0 and 3 for nonzero leakage. In the noisy comparison, spectral radius fell from 1.29825 to 0.90145, while 10-step MSE only changed from 0.085465 to 0.085447, so stability filtering is real but an accuracy gain was not demonstrated.",
  "metrics": {
    "baseline": "Toy/noisy mean spectral radius 1.29825; 10-step rollout MSE 0.0854648; 30-step nuisance rollout norm 2619.996",
    "idea": "Toy/noisy mean spectral radius 0.90145; 10-step rollout MSE 0.0854467; 30-step filtered rollout norm 0.04240; supported-eigenvalue error <=2.22e-16"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 forward_intersection.py && /home/maxwelhelp/main/bin/python3 mini_experiment.py",
  "files": [
    "forward_intersection.py",
    "mini_experiment.py"
  ],
  "limitations": "No neural encoder or learned nonlinear world model was trained; the experiment uses a hand-constructed linear toy with one unstable nuisance mode and a small noisy least-squares snapshot test. It does not test computational overhead, multi-level learned refresh schedules, Lorenz/pendulum data, or generalization beyond the supported-mode setup."
}